Continuous topological charge manipulation with radially varying polarizations

Topological charge (m), a fundamental quantity characterizing optical orbital angular momentum (OAM), has been intensively studied primarily as a discrete integer. However, realizing topological charges with arbitrary, continuous values remains a significant challenge in structured light fields. In this work, we demonstrate that continuous tuning of the effective topological charge (meff) can be achieved by designing a radially varying state of polarization (SOP) in a perfect vector vortex beam. Our approach utilizes the synergistic coupling between the beam's azimuthal phase and the engineered radial polarization gradient. Both theoretical calculations and experimental results show that the magnitude and sign of meff are precisely determined by two key parameters: a phase-dependent parameter controlling the local SOP and the beam's waist radius. The high precision of this control is validated through optical tweezer experiments, where the angular velocities of trapped particles are shown to scale linearly with the continuously adjustable meff. This work not only breaks the conventional discreteness barriers of OAM but also offers a highly versatile platform for advanced applications in light field manipulation and dynamical microparticle control.